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Distances on Lie groups of polynomial volume growth

โœ Scribed by Nourredine Bounechada


Publisher
Springer-Verlag
Year
2005
Tongue
French
Weight
175 KB
Volume
251
Category
Article
ISSN
0025-5874

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๐Ÿ“œ SIMILAR VOLUMES


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Let G be a Lie group of polynomial growth. We prove that the second-order Riesz transforms on L 2 (G ; dg) are bounded if, and only if, the group is a direct product of a compact group and a nilpotent group, in which case the transforms of all orders are bounded.

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## Abstract We introduce a Littlewoodโ€“Paley decomposition related to any subโ€Laplacian on a Lie group __G__ of polynomial volume growth; this allows us to prove a Littlewoodโ€“Paley theorem in this general setting and to provide a dyadic characterization of Besov spaces __B__ ^__s,q__^ ~__p__~ (__G_

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We give the Bernstein polynomials for basic matrix entries of irreducible unitary ลฝ . representations of compact Lie group SU 2 . We also give an application to the ลฝ . analytic continuation of certain distributions on SU 2 , and finally we briefly describe the Bernstein polynomial for B = B-semi-in